微積分求這兩題題目解法答案 謝謝?
回答 (1)
2017-12-25 6:18 am
1
lim(x->0)_Sin(3x)/Sin(2x) 0/0 type
=lim(x->0)_3Cos(3x)/[2Cos(2x)]
=3/2
2
Sol
y=ArcTan[√(x^2－1)[
Tany=√(x^2－1)
Tan^2 y=x^2－1
dSec^2 y=x^2
dx^2/dx=dsSc^2 y/dx
2x=(dSec^2 y/dSecy)*(dSecy/dy)*(dy/dx)
=2Secy*Secy*Tany*(dy/dx)
=2Sec^2 y*Tany*(dy/dx)
=2(Tan^2 y+1)*Tany*(dy/dx)
=2*x^2*√(x^2－1)*(dy/dx)
dy/dx=1/[x√(x^2－1)]
lim(x->0)_Sin(3x)/Sin(2x) 0/0 type
=lim(x->0)_3Cos(3x)/[2Cos(2x)]
=3/2
2
Sol
y=ArcTan[√(x^2－1)[
Tany=√(x^2－1)
Tan^2 y=x^2－1
dSec^2 y=x^2
dx^2/dx=dsSc^2 y/dx
2x=(dSec^2 y/dSecy)*(dSecy/dy)*(dy/dx)
=2Secy*Secy*Tany*(dy/dx)
=2Sec^2 y*Tany*(dy/dx)
=2(Tan^2 y+1)*Tany*(dy/dx)
=2*x^2*√(x^2－1)*(dy/dx)
dy/dx=1/[x√(x^2－1)]
收錄日期: 2021-04-30 22:29:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20171224122410AApl3rU